Lecture Notes: Quantum Mechanics and Orbitals
Introduction to Orbitals
- Orbital Definition: The most probable location to find an electron.
- Bohr Model of the Atom: Circular orbits representing energy levels.
Energy Levels and Quantum Numbers
- Principal Quantum Number (n)
- Represents the energy level and size of the orbital.
- As "n" increases, the distance from the nucleus increases.
- Lower "n" values indicate electrons closer to the nucleus with lower energy.
Angular Momentum Quantum Number (L)
- Describes the shape of the orbital
- L = 0: s orbital (spherical shape)
- L = 1: p orbital (dumbbell shape)
- L = 2: d orbital (cloverleaf shape)
- L = 3: f orbital (complex shape)
- Sublevel Correspondence
- L values determine sublevels: s, p, d, f
Relationship Between n and L
- L ≤ n-1
- n = 1: Only s sub-level (L=0)
- n = 2: S and P sub-levels (L=0, 1)
- n = 3: S, P, and D sub-levels (L=0, 1, 2)
- n = 4: S, P, D, and F sub-levels (L=0, 1, 2, 3)
Magnetic Quantum Number (M<sub>L</sub>)
- Describes the orientation of the orbital
- For s sub-level: L=0, hence M<sub>L</sub>=0
- For p sub-level: L=1, M<sub>L</sub> varies between -1 and 1
- For d sub-level: L=2, M<sub>L</sub> varies between -2 and 2
Electron Spin Quantum Number (M<sub>S</sub>)
- Electron Spin
- Two possibilities: +1/2 (up spin) or -1/2 (down spin)
- Pauli’s Exclusion Principle
- Each electron in an atom has a unique set of four quantum numbers.
Examples
Conclusion
- Engage with additional resources for further understanding.
- Recommended further videos on quantum numbers and electron configurations.
For more examples and detailed explanations, visit the speaker's YouTube channel for a comprehensive chemistry playlist.